Signal downconversion is an important aspect of many electronic systems. For example, in many communications systems, signals modulated on relatively high frequency carrier signals are downconverted to lower frequency baseband and then further processed.
Downconversion is sometimes implemented by mixing the modulated signal with another signal generated by a local oscillator (LO). The frequency of the local oscillator signal is typically set to be the same as the carrier frequency of the modulated complex signal. The resulting signal is then low pass filtered and sampled to generate a baseband signal centered at approximately 0 Hz or DC. However, such an implementation is sometimes impractical because the circuit generally requires a dedicated analog mixer that is often implemented as a discrete component. The inclusion of the analog mixer may increase the complexity and production cost of the receivers.
FIG. 1 is a block diagram illustrating a digital receiver circuit that eliminates the analog mixer. In this example, a modulated complex input signal 110 (denoted as x(t)) is undersampled by an analog-to-digital converter (ADC). Signal 120 (denoted as s(T)) is the sampling signal used by the ADC. Digital mixer 102 performs a quadrature demodulation on undersampled output 112 (denoted as z(n)) by multiplying z(n) with a complex local oscillator signal 114 (denoted as L(n)). Mixer output 116 is then low pass filtered by filter 104 to obtain a baseband signal 118 (denoted as x(n)).
FIG. 2A is a plot illustrating the frequency spectrum of a complex modulated signal (x(t) shown in FIG. 1). The carrier frequency of the signal in this example is ωc. The signal is shown to have a positive image 200 and a negative image 202. FIG. 2B is a plot illustrating the frequency spectrum of an undersampled modulated signal (z(n) shown in FIG. 1). The fundamental frequency of the sampling signal used in this example, s(T), is lower than the carrier frequency of x(t). Because the sampling signal includes harmonic frequencies, the undersampled output 112 includes replicas of the modulated signal occurring at regular intervals. FIG. 2C is a diagram illustrating the frequency spectrum of a demodulated signal (signal 116 shown in FIG. 1). After the mixing, the modulated signal replicas are shifted and one of the positive image replicas is translated to baseband. The signal is then low pass filtered to obtain a baseband signal 204.
While undersampling a complex modulated signal can eliminate the analog quadrature mixing stage, the circuit still requires a digital quadrature mixer after the signal is sampled. It would be useful to be able to convert a complex modulated signal to a baseband signal without requiring a digital mixer. It would also be useful if the conversion would not introduce much distortion due to aliasing between positive and negative images of the complex modulated signal.